Robust sequential testing
type: Item
instance of: scholarly article
title: Robust sequential testing
zbMATH Open document ID: 0588.62136
author: Pham Xuan Quang
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: The author considers the asymptotic minimax property of the sequential probability ratio test (SPRT) when the given distributions \(P_{+\epsilon}\) and \(P_{-\epsilon}\) contain a small amount of contamination. Let \(N_{+\epsilon}\) and \(N_{-\epsilon}\) be the neighborhoods of \(P_{+\epsilon}\) and \(P_{-\epsilon}\), respectively. Suppose that \(P_{\epsilon}\) and \(P_{-\epsilon}\) approach each other as \(\epsilon\) tends to zero and that \(N_{+\epsilon}\) and \(N_{- \epsilon}\) shrink at an appropriate rate. Under suitable regularity conditions it is proved that the SPRT based on the least favorable pair of distributions \((Q_{+\epsilon},Q_{- \epsilon})\) as defined by \textit{P. J. Huber} [Ann. Math. Stat. 36, 1753- 1758 (1965; Zbl 0137.127)] is asymptotically least favorable for expected sample size and is asymptotically minimax, provided that the limiting maximum error probabilities are no greater than 1/2.
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62F35
zbMATH DE Number: 3945162
zbMATH Keywords: shrinking neighborhoods
zbMATH Keywords: asymptotic minimax property
zbMATH Keywords: sequential probability ratio test
zbMATH Keywords: contamination
zbMATH Keywords: asymptotically least favorable
reviewed by: Volker Mammitzsch
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349544
OpenAlex ID: W1979660604
DOI: 10.1214/AOS/1176349544
description: scientific article; zbMATH DE number 3945162